This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##   [1] "beta0_pH"       "re_pelagic"     "p_yellow"       "pDSR_YE_ayu"   
##   [5] "pDSR_YE_ay"     "re_pH"          "re_yellow"      "beta1_pH"      
##   [9] "pDSR_YE_ayg"    "mu_beta1_pH"    "Hdnye_ay"       "Hdnye_ayg"     
##  [13] "Tdnye_ayg"      "beta3_pH"       "Bdnye_ayg"      "Hy_ay"         
##  [17] "beta2_pH"       "Ry_ayg"         "Ry_ayg_mort"    "mu_beta2_pH"   
##  [21] "Hy_ayu"         "R_ayg"          "Rb_ayg"         "Rb_ayg_mort"   
##  [25] "Tb_ayg"         "Rp_ayg"         "Rp_ayg_mort"    "Bp_ayg"        
##  [29] "Tp_ayg"         "Bb_ayg"         "R_ay"           "Rb_ay"         
##  [33] "Rb_ay_mort"     "Tb_ay"          "Rp_ay"          "Rp_ay_mort"    
##  [37] "Tp_ay"          "Bp_ay"          "Bb_ay"          "By_ayg"        
##  [41] "Ry_ay_mort"     "Ry_ay"          "Ty_ayg"         "Rd_ayg"        
##  [45] "R_ayu"          "Rb_ayu"         "Rb_ayu_mort"    "Bp_ayu"        
##  [49] "Rp_ayu"         "Rp_ayu_mort"    "Tb_ayu"         "Bb_ayu"        
##  [53] "Tp_ayu"         "Ty_ay"          "Ry_ayu"         "Ry_ayu_mort"   
##  [57] "Ty_ayu"         "By_ay"          "Rd_ay"          "tau_beta1_pH"  
##  [61] "Rd_ayu"         "By_ayu"         "p_dsr"          "Hd_ayg"        
##  [65] "Rs_ayu"         "Rs_ayu_mort"    "Rs_ayg"         "Rs_ayg_mort"   
##  [69] "Rdnye_ayu"      "Rdnye_ayu_mort" "Ro_ayu"         "Rdnye_ay"      
##  [73] "Rdnye_ay_mort"  "Ro_ay"          "Tdnye_ay"       "Ro_ayg"        
##  [77] "Rdnye_ayg_mort" "Rdnye_ayg"      "pH"             "Bdnye_ay"      
##  [81] "Rs_ay"          "Rs_ay_mort"     "tau_beta0_pH"   "Hd_ay"         
##  [85] "re_dsr"         "p_pelagic"      "Hy_ayg"         "Tdnye_ayu"     
##  [89] "Bdnye_ayu"      "Ho_ayg"         "Ho_ay"          "beta4_pH"      
##  [93] "tau_beta2_pH"   "mu_beta0_pH"    "H_ayu"          "H_ay"          
##  [97] "Hdnye_ayu"      "Hp_ay"          "Hp_ayu"         "Hb_ayu"        
## [101] "Hb_ay"          "Hd_ayu"         "mu2_wt"         "Bs_ayu"        
## [105] "H_ayg"          "Ho_ayu"         "Ts_ayu"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 4 1.880784
beta0_yellow 8 1.842631
beta1_yellow 8 1.748071
beta2_yellow 4 1.540806
mu_beta0_yellow 1 1.421970
beta2_pelagic 5 1.419462
beta0_pelagic 6 1.382684
beta1_pelagic 7 1.379290
tau_beta0_yellow 2 1.358255
parameter n badRhat_avg
beta3_pelagic 5 1.356240
beta1_pH 27 1.344262
beta0_pH 19 1.302444
beta3_pH 17 1.205937
beta2_pH 13 1.195136
tau_beta0_pH 5 1.176446
beta4_pelagic 1 1.164873
mu_beta0_pH 2 1.155487
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta0_pH 1 0 0 0 0 1 0 1 1 1 1 2 3 3 2 3
beta0_pH 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1
beta1_pH 1 1 1 1 1 1 1 1 1 1 2 3 3 3 3 3
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta2_pH 2 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1
beta2_pH 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1
beta3_pH 0 0 1 1 0 0 0 0 0 0 3 2 3 3 2 2
beta3_pH 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1
beta4_pH 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0
Bp_ay 0 0 0 0 0 0 0 0 0 0 6 8 14 11 13 14
Bp_ayg 0 0 0 0 0 0 0 0 0 0 6 7 13 11 11 10
Bp_ayu 0 0 0 0 0 0 0 0 0 0 8 11 12 11 10 10
H_ay 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
H_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
H_ayu 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
Hb_ay 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 4
Hb_ayu 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 3
Hd_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1
Hd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
Hd_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
Hdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1
Ho_ay 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
Ho_ayg 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0
Ho_ayu 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
Hp_ay 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 4
Hp_ayu 0 0 0 0 1 0 0 0 0 0 2 0 1 0 0 3
Hy_ay 0 0 0 0 1 0 0 0 0 0 0 1 0 2 0 2
Hy_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 1
Hy_ayu 0 0 0 0 1 0 0 0 1 0 0 4 0 2 0 2
mu_beta0_pH 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta1_pH 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta2_pH 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 43 0 5 0 0
p_pelagic 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 33
p_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 6 0 6
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 3
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 3
pH 0 2 3 1 5 6 0 1 22 16 2 26 20 6 14 7
R_ay 13 12 11 13 15 20 10 11 14 12 9 8 13 11 13 11
R_ayg 12 11 12 13 15 12 9 10 12 13 10 7 12 12 13 10
R_ayu 11 11 10 11 16 18 14 10 13 11 6 10 11 13 10 10
Rb_ay 12 12 11 13 14 20 10 11 14 11 12 8 13 14 11 12
Rb_ay_mort 12 13 12 15 14 20 10 11 14 11 12 8 13 14 11 12
Rb_ayg 13 12 12 14 15 13 9 10 12 12 11 7 12 12 10 10
Rb_ayg_mort 13 12 12 14 15 13 9 10 12 12 11 7 12 12 10 10
Rb_ayu 10 11 12 13 15 18 14 14 14 11 23 11 10 14 11 11
Rb_ayu_mort 10 11 12 13 15 18 14 14 14 11 23 11 10 14 11 11
Rd_ay 0 0 0 0 0 0 0 0 0 0 1 13 12 13 9 9
Rd_ayg 0 0 0 0 0 0 0 0 0 0 5 17 13 13 10 12
Rd_ayu 0 0 0 0 0 0 0 0 0 0 0 10 2 5 1 1
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 1 21 0 1 2 0
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 1 21 0 1 2 0
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 4 19 0 4 1 0
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 4 19 0 4 1 0
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 2 22 0 1 2 0
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 2 22 0 1 2 0
re_pelagic 0 0 0 7 0 0 0 0 0 0 19 1 20 0 15 38
re_pH 26 0 0 7 0 0 0 12 28 26 21 17 44 35 41 32
Ro_ay 0 1 0 3 3 2 0 2 1 1 0 21 0 1 2 0
Ro_ayg 1 0 0 1 3 2 2 2 2 0 4 19 2 4 2 0
Ro_ayu 0 1 0 3 3 2 0 2 1 1 0 22 0 1 2 0
Rp_ay 13 12 11 13 15 20 10 11 14 12 15 8 13 14 14 12
Rp_ay_mort 12 12 11 13 15 20 10 11 13 12 15 8 13 14 14 12
Rp_ayg 12 11 12 13 15 12 9 10 12 13 11 7 12 12 11 10
Rp_ayg_mort 12 11 12 13 15 12 9 10 12 13 11 7 12 12 11 10
Rp_ayu 11 11 10 12 16 18 14 12 14 11 23 11 11 14 12 11
Rp_ayu_mort 11 11 10 12 16 18 14 12 14 11 23 11 11 14 12 11
Rs_ay 0 0 0 0 0 0 0 0 0 0 1 29 0 1 1 0
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 1 29 0 1 1 0
Rs_ayg 0 0 0 0 0 0 0 0 0 0 4 14 0 2 0 0
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 4 14 0 2 0 0
Rs_ayu 0 0 0 0 0 0 0 0 0 0 0 27 0 1 2 0
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 27 0 1 2 0
Ry_ay 2 9 5 13 32 30 17 6 19 8 1 14 12 13 9 11
Ry_ay_mort 3 10 5 13 32 30 17 6 19 8 1 14 12 13 9 11
Ry_ayg 20 16 15 14 22 22 17 19 25 26 6 20 24 14 17 18
Ry_ayg_mort 20 16 15 14 22 22 17 19 25 26 6 20 24 14 17 18
Ry_ayu 4 3 3 9 29 29 18 6 15 6 1 10 4 6 4 2
Ry_ayu_mort 4 3 3 9 29 29 18 6 15 6 1 10 4 6 4 2
tau_beta0_pH 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta1_pH 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta2_pH 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ay 12 10 11 11 11 13 9 11 12 12 4 8 14 11 13 15
Tp_ayg 12 10 12 12 13 12 9 10 12 13 4 7 12 11 11 9
Tp_ayu 7 1 10 5 11 10 10 9 12 11 8 10 12 12 10 10
beta0_pelagic 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1
beta0_yellow 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1
beta1_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1
beta1_yellow 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1
beta2_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1
beta2_yellow 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1
beta3_yellow 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
mu_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.154 0.071 -0.289 -0.157 -0.012
mu_bc_H[2] -0.126 0.038 -0.198 -0.128 -0.043
mu_bc_H[3] -0.453 0.071 -0.584 -0.454 -0.309
mu_bc_H[4] -1.086 0.203 -1.485 -1.085 -0.698
mu_bc_H[5] 0.778 0.918 -0.318 0.616 2.950
mu_bc_H[6] -2.215 0.302 -2.790 -2.225 -1.616
mu_bc_H[7] -0.491 0.108 -0.706 -0.489 -0.281
mu_bc_H[8] 0.071 0.300 -0.439 0.043 0.782
mu_bc_H[9] -0.358 0.144 -0.637 -0.358 -0.079
mu_bc_H[10] -0.140 0.065 -0.260 -0.144 -0.008
mu_bc_H[11] -0.150 0.039 -0.231 -0.148 -0.078
mu_bc_H[12] -0.275 0.110 -0.524 -0.266 -0.083
mu_bc_H[13] -0.241 0.082 -0.409 -0.237 -0.085
mu_bc_H[14] -0.362 0.107 -0.584 -0.358 -0.165
mu_bc_H[15] -0.375 0.049 -0.471 -0.374 -0.278
mu_bc_H[16] -0.666 0.370 -1.319 -0.681 0.118
mu_bc_R[1] 1.466 0.149 1.183 1.461 1.766
mu_bc_R[2] 1.522 0.088 1.356 1.520 1.704
mu_bc_R[3] 1.442 0.149 1.150 1.442 1.725
mu_bc_R[4] 1.112 0.182 0.726 1.124 1.432
mu_bc_R[5] 1.660 0.508 0.663 1.663 2.660
mu_bc_R[6] -0.987 0.540 -2.028 -0.972 0.063
mu_bc_R[7] 0.455 0.154 0.148 0.456 0.739
mu_bc_R[8] 0.575 0.194 0.195 0.574 0.956
mu_bc_R[9] 0.534 0.166 0.168 0.542 0.837
mu_bc_R[10] 1.519 0.132 1.257 1.520 1.785
mu_bc_R[11] 1.057 0.117 0.837 1.057 1.293
mu_bc_R[12] 0.913 0.203 0.539 0.908 1.334
mu_bc_R[13] 1.105 0.106 0.906 1.104 1.314
mu_bc_R[14] 0.947 0.146 0.650 0.947 1.235
mu_bc_R[15] 0.890 0.119 0.665 0.888 1.130
mu_bc_R[16] 1.151 0.133 0.899 1.145 1.421
tau_pH[1] 0.109 0.098 0.040 0.066 0.369
tau_pH[2] 1.539 0.679 0.133 1.810 2.350
tau_pH[3] 1.994 0.444 0.903 2.061 2.735
beta0_pH[1,1] 4.083 1.531 1.861 3.940 7.443
beta0_pH[2,1] 7.816 1.877 4.205 7.938 10.906
beta0_pH[3,1] 5.462 1.671 2.721 5.429 8.660
beta0_pH[4,1] 4.861 1.349 2.755 4.670 7.743
beta0_pH[5,1] 2.233 1.022 0.583 2.128 4.312
beta0_pH[6,1] 1.327 0.715 0.112 1.278 2.928
beta0_pH[7,1] 3.017 1.642 -0.353 3.184 5.540
beta0_pH[8,1] 3.638 1.823 0.526 4.110 6.780
beta0_pH[9,1] 2.104 1.315 0.153 2.022 4.601
beta0_pH[10,1] 3.826 2.080 0.928 3.389 7.405
beta0_pH[11,1] 9.934 2.028 5.127 10.310 12.943
beta0_pH[12,1] 3.338 0.764 2.076 3.342 5.164
beta0_pH[13,1] 6.399 2.082 2.988 5.851 10.626
beta0_pH[14,1] 4.101 1.579 1.720 3.867 7.242
beta0_pH[15,1] 6.883 2.120 2.934 7.265 10.171
beta0_pH[16,1] 6.372 2.024 3.079 6.690 10.110
beta0_pH[1,2] 2.876 0.235 2.464 2.862 3.446
beta0_pH[2,2] 2.900 0.232 2.525 2.887 3.481
beta0_pH[3,2] 3.142 0.207 2.802 3.125 3.651
beta0_pH[4,2] 3.009 0.218 2.680 2.981 3.574
beta0_pH[5,2] 4.650 1.458 2.884 4.329 8.522
beta0_pH[6,2] 3.174 0.320 2.651 3.141 3.954
beta0_pH[7,2] 1.866 0.324 1.333 1.836 2.717
beta0_pH[8,2] 2.901 0.275 2.449 2.876 3.610
beta0_pH[9,2] 3.500 0.317 2.975 3.475 4.228
beta0_pH[10,2] 3.630 0.286 3.141 3.604 4.309
beta0_pH[11,2] -2.889 3.445 -5.461 -4.703 8.058
beta0_pH[12,2] -3.856 1.902 -5.461 -4.609 1.054
beta0_pH[13,2] -3.543 2.006 -5.229 -4.348 1.590
beta0_pH[14,2] -4.235 2.346 -6.427 -5.185 1.817
beta0_pH[15,2] -3.212 2.024 -4.874 -4.100 1.899
beta0_pH[16,2] -3.663 2.195 -5.474 -4.570 1.918
beta0_pH[1,3] -0.451 0.798 -2.056 -0.428 1.109
beta0_pH[2,3] 2.193 0.171 1.862 2.198 2.526
beta0_pH[3,3] 2.527 0.165 2.219 2.524 2.861
beta0_pH[4,3] 2.960 0.175 2.619 2.959 3.302
beta0_pH[5,3] 1.034 0.586 0.158 0.955 2.386
beta0_pH[6,3] 0.608 0.599 -0.599 0.666 1.683
beta0_pH[7,3] 0.669 0.192 0.304 0.665 1.057
beta0_pH[8,3] 0.307 0.208 -0.116 0.308 0.703
beta0_pH[9,3] -0.507 0.450 -1.707 -0.482 0.288
beta0_pH[10,3] 0.477 0.417 -0.617 0.533 1.152
beta0_pH[11,3] -0.173 0.757 -1.541 -0.325 1.596
beta0_pH[12,3] -0.660 0.798 -1.672 -0.819 1.816
beta0_pH[13,3] 0.044 0.655 -1.147 -0.082 1.505
beta0_pH[14,3] -0.133 0.569 -0.872 -0.275 1.465
beta0_pH[15,3] -0.381 1.240 -1.666 -0.719 3.050
beta0_pH[16,3] -0.297 0.642 -1.190 -0.477 1.243
beta1_pH[1,1] 0.173 0.510 0.000 0.000 2.006
beta1_pH[2,1] 0.155 0.537 0.000 0.000 1.717
beta1_pH[3,1] 0.202 0.500 0.000 0.000 1.907
beta1_pH[4,1] 0.714 1.374 0.000 0.000 4.583
beta1_pH[5,1] 0.275 0.543 0.000 0.015 2.038
beta1_pH[6,1] 0.190 0.428 0.000 0.010 1.857
beta1_pH[7,1] 0.490 0.944 0.000 0.016 3.399
beta1_pH[8,1] 0.146 0.308 0.000 0.010 1.060
beta1_pH[9,1] 1.160 2.095 0.000 0.119 9.022
beta1_pH[10,1] 1.031 1.619 0.000 0.067 5.457
beta1_pH[11,1] 0.014 0.063 0.000 0.000 0.181
beta1_pH[12,1] 0.013 0.056 0.000 0.000 0.176
beta1_pH[13,1] 0.017 0.108 0.000 0.000 0.127
beta1_pH[14,1] 0.102 0.577 0.000 0.000 1.865
beta1_pH[15,1] 0.013 0.071 0.000 0.000 0.126
beta1_pH[16,1] 0.023 0.115 0.000 0.000 0.396
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.001 0.000 0.000 0.000
beta1_pH[4,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 5.023 2.402 0.000 6.410 7.154
beta1_pH[12,2] 5.344 2.136 0.000 6.172 7.150
beta1_pH[13,2] 5.674 2.352 0.000 6.624 7.672
beta1_pH[14,2] 5.784 2.450 0.000 6.783 8.033
beta1_pH[15,2] 5.472 2.373 0.000 6.521 7.371
beta1_pH[16,2] 6.009 2.532 0.000 7.054 8.022
beta1_pH[1,3] 5.063 1.808 1.979 4.944 8.751
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 2.968 1.517 1.027 2.710 6.978
beta1_pH[6,3] 2.396 1.350 0.537 2.238 5.628
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.711 0.412 1.929 2.695 3.542
beta1_pH[9,3] 2.644 0.513 1.752 2.607 3.878
beta1_pH[10,3] 2.848 0.517 1.983 2.790 4.148
beta1_pH[11,3] 2.573 1.101 0.000 2.832 4.299
beta1_pH[12,3] 3.777 1.164 0.000 4.048 5.063
beta1_pH[13,3] 1.454 0.681 0.000 1.592 2.544
beta1_pH[14,3] 2.301 0.800 0.000 2.495 3.261
beta1_pH[15,3] 1.723 0.916 0.000 1.957 2.822
beta1_pH[16,3] 1.609 0.721 0.000 1.822 2.522
beta2_pH[1,1] -1.942 8.014 -18.858 -2.319 17.123
beta2_pH[2,1] -1.821 8.518 -19.665 -2.044 17.564
beta2_pH[3,1] -1.915 8.452 -19.228 -2.061 17.084
beta2_pH[4,1] -1.653 8.383 -18.857 -1.589 18.050
beta2_pH[5,1] 0.243 2.644 -5.350 0.171 6.065
beta2_pH[6,1] 0.148 2.681 -5.596 0.109 6.315
beta2_pH[7,1] 0.309 3.743 0.000 0.000 0.281
beta2_pH[8,1] 0.506 2.527 -5.122 0.351 5.937
beta2_pH[9,1] 0.011 2.442 -5.920 0.509 4.991
beta2_pH[10,1] 0.216 2.368 -5.000 0.062 5.329
beta2_pH[11,1] 2.980 8.820 -15.846 4.231 17.998
beta2_pH[12,1] 2.968 8.814 -15.656 4.043 18.305
beta2_pH[13,1] 2.901 8.842 -15.757 4.035 18.512
beta2_pH[14,1] 2.900 8.878 -16.065 4.142 18.758
beta2_pH[15,1] 3.098 8.889 -15.701 4.187 18.955
beta2_pH[16,1] 3.167 8.687 -15.535 5.021 18.007
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.015 1.810 -6.883 -1.521 -0.032
beta2_pH[4,2] -1.970 1.821 -6.821 -1.507 -0.021
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -10.539 6.064 -24.602 -9.701 0.763
beta2_pH[12,2] -9.890 6.277 -24.593 -9.170 0.601
beta2_pH[13,2] -9.720 6.368 -24.899 -8.936 0.810
beta2_pH[14,2] -10.212 6.197 -24.421 -9.487 1.107
beta2_pH[15,2] -10.549 6.071 -25.231 -9.731 1.080
beta2_pH[16,2] -10.677 6.045 -25.045 -9.918 0.431
beta2_pH[1,3] 0.354 1.061 0.100 0.148 4.181
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.316 6.263 0.576 8.343 23.749
beta2_pH[6,3] 8.942 6.499 0.157 7.798 24.141
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 9.922 5.994 1.216 8.797 24.408
beta2_pH[9,3] 9.140 6.375 0.497 8.073 24.094
beta2_pH[10,3] 8.630 6.622 0.435 7.659 24.102
beta2_pH[11,3] -2.508 4.065 -14.036 -1.583 2.013
beta2_pH[12,3] -2.642 3.832 -13.797 -1.818 2.195
beta2_pH[13,3] -3.000 4.088 -14.345 -2.035 1.859
beta2_pH[14,3] -3.012 4.047 -14.014 -2.069 2.509
beta2_pH[15,3] -3.223 4.092 -14.615 -2.181 2.753
beta2_pH[16,3] -3.166 4.096 -14.130 -2.189 2.290
beta3_pH[1,1] 28.985 7.683 18.372 27.781 44.180
beta3_pH[2,1] 28.746 7.771 18.370 27.027 44.290
beta3_pH[3,1] 32.060 7.691 18.730 33.051 44.555
beta3_pH[4,1] 29.148 7.185 18.571 27.602 44.540
beta3_pH[5,1] 30.202 8.007 18.369 29.474 44.928
beta3_pH[6,1] 30.049 8.041 18.370 29.164 44.846
beta3_pH[7,1] 30.009 7.873 18.396 29.062 44.823
beta3_pH[8,1] 30.570 7.812 18.537 29.882 44.864
beta3_pH[9,1] 28.903 7.479 18.234 28.578 44.404
beta3_pH[10,1] 29.423 7.590 18.712 27.156 44.635
beta3_pH[11,1] 34.921 4.727 29.179 33.290 45.138
beta3_pH[12,1] 37.096 4.683 29.377 36.863 45.553
beta3_pH[13,1] 36.583 4.903 29.294 37.026 45.429
beta3_pH[14,1] 39.172 5.015 29.479 40.483 45.725
beta3_pH[15,1] 37.296 4.914 29.439 37.004 45.494
beta3_pH[16,1] 36.689 5.022 29.239 36.206 45.427
beta3_pH[1,2] 30.028 7.890 18.509 29.147 44.799
beta3_pH[2,2] 29.905 8.041 18.469 28.876 44.836
beta3_pH[3,2] 29.911 7.889 18.521 29.075 44.576
beta3_pH[4,2] 30.034 7.906 18.517 29.136 44.880
beta3_pH[5,2] 30.204 7.982 18.560 29.355 44.993
beta3_pH[6,2] 30.005 7.996 18.425 29.053 44.927
beta3_pH[7,2] 30.013 7.896 18.447 28.935 44.839
beta3_pH[8,2] 29.622 7.911 18.508 28.469 44.876
beta3_pH[9,2] 30.116 7.995 18.364 29.231 44.927
beta3_pH[10,2] 30.129 8.123 18.446 29.066 45.174
beta3_pH[11,2] 42.145 2.708 32.869 43.336 43.845
beta3_pH[12,2] 42.357 2.687 32.600 43.126 43.833
beta3_pH[13,2] 42.971 2.884 31.808 43.908 44.073
beta3_pH[14,2] 42.487 2.568 33.040 43.206 43.892
beta3_pH[15,2] 42.734 2.407 33.553 43.345 43.904
beta3_pH[16,2] 42.523 2.982 31.494 43.456 43.882
beta3_pH[1,3] 38.332 3.748 30.645 38.516 45.254
beta3_pH[2,3] 30.124 7.880 18.448 29.371 44.703
beta3_pH[3,3] 30.273 7.921 18.478 29.527 45.056
beta3_pH[4,3] 30.393 8.081 18.512 29.601 45.015
beta3_pH[5,3] 40.959 3.499 32.573 41.942 45.249
beta3_pH[6,3] 37.782 4.664 31.169 38.401 45.432
beta3_pH[7,3] 37.975 4.291 31.348 37.697 45.511
beta3_pH[8,3] 41.499 0.423 40.914 41.500 41.979
beta3_pH[9,3] 33.500 0.597 31.686 33.578 34.472
beta3_pH[10,3] 35.783 0.869 33.302 36.003 36.885
beta3_pH[11,3] 41.597 2.449 32.723 42.171 43.687
beta3_pH[12,3] 41.372 1.905 34.220 41.727 42.639
beta3_pH[13,3] 42.124 2.795 31.615 42.691 45.382
beta3_pH[14,3] 40.850 1.819 34.539 41.171 42.403
beta3_pH[15,3] 41.595 3.001 31.124 42.734 43.916
beta3_pH[16,3] 42.185 2.875 30.911 43.013 44.237
beta0_pelagic[1] 2.202 0.131 1.952 2.199 2.462
beta0_pelagic[2] 1.435 0.112 1.213 1.432 1.660
beta0_pelagic[3] -0.217 0.529 -1.376 -0.050 0.467
beta0_pelagic[4] 0.305 0.376 -0.392 0.309 1.034
beta0_pelagic[5] 1.152 0.252 0.657 1.156 1.650
beta0_pelagic[6] 1.431 0.287 0.833 1.455 1.948
beta0_pelagic[7] 1.634 0.206 1.249 1.619 2.078
beta0_pelagic[8] 1.708 0.191 1.332 1.709 2.087
beta0_pelagic[9] 2.432 0.300 1.843 2.436 2.980
beta0_pelagic[10] 2.468 0.197 2.038 2.479 2.829
beta0_pelagic[11] -0.292 0.382 -1.127 -0.176 0.271
beta0_pelagic[12] 1.641 0.148 1.354 1.643 1.931
beta0_pelagic[13] 0.151 0.224 -0.223 0.142 0.580
beta0_pelagic[14] -0.111 0.255 -0.709 -0.097 0.370
beta0_pelagic[15] -0.378 0.147 -0.670 -0.366 -0.117
beta0_pelagic[16] -0.037 0.312 -0.672 -0.047 0.474
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.415 0.573 0.548 1.280 2.640
beta1_pelagic[4] 1.099 0.495 0.237 1.138 2.107
beta1_pelagic[5] -0.080 0.309 -0.689 -0.078 0.531
beta1_pelagic[6] -0.166 0.506 -0.980 -0.270 0.778
beta1_pelagic[7] -0.028 0.295 -0.575 -0.038 0.567
beta1_pelagic[8] -0.008 0.252 -0.504 -0.007 0.471
beta1_pelagic[9] 0.263 0.476 -0.735 0.381 0.975
beta1_pelagic[10] 0.063 0.279 -0.470 0.060 0.618
beta1_pelagic[11] 3.477 0.701 2.270 3.469 4.914
beta1_pelagic[12] 2.904 0.381 2.259 2.869 3.823
beta1_pelagic[13] 3.390 0.915 1.919 3.325 5.370
beta1_pelagic[14] 4.509 1.008 3.002 4.288 6.676
beta1_pelagic[15] 3.092 0.295 2.487 3.090 3.671
beta1_pelagic[16] 4.146 0.720 2.869 4.211 5.516
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.624 2.011 0.080 0.208 5.148
beta2_pelagic[4] 1.949 3.821 0.053 0.325 14.326
beta2_pelagic[5] -0.028 0.679 -1.440 -0.020 1.384
beta2_pelagic[6] -0.159 0.718 -1.551 -0.232 1.350
beta2_pelagic[7] 0.018 0.643 -1.348 0.009 1.373
beta2_pelagic[8] -0.007 0.651 -1.422 -0.003 1.394
beta2_pelagic[9] 0.256 0.685 -1.225 0.312 1.615
beta2_pelagic[10] 0.046 0.660 -1.304 0.048 1.438
beta2_pelagic[11] 0.221 0.060 0.129 0.216 0.340
beta2_pelagic[12] 3.684 3.073 0.559 2.887 12.326
beta2_pelagic[13] 0.509 0.526 0.160 0.343 2.016
beta2_pelagic[14] 0.309 0.113 0.168 0.283 0.621
beta2_pelagic[15] 3.667 2.799 0.742 3.023 11.085
beta2_pelagic[16] 1.260 2.389 0.193 0.357 8.650
beta3_pelagic[1] 29.684 7.815 18.462 28.648 44.887
beta3_pelagic[2] 29.763 7.996 18.384 28.689 45.163
beta3_pelagic[3] 28.319 5.279 19.011 28.354 39.335
beta3_pelagic[4] 28.561 6.482 19.892 26.463 45.069
beta3_pelagic[5] 30.115 8.159 18.517 28.885 45.125
beta3_pelagic[6] 31.519 6.181 19.322 31.207 43.879
beta3_pelagic[7] 29.675 7.689 18.508 28.595 45.007
beta3_pelagic[8] 29.623 7.970 18.418 28.463 44.817
beta3_pelagic[9] 30.686 5.947 19.305 30.644 42.847
beta3_pelagic[10] 29.432 8.179 18.317 27.902 44.851
beta3_pelagic[11] 38.914 2.681 33.277 38.806 43.566
beta3_pelagic[12] 43.491 0.361 42.901 43.462 44.266
beta3_pelagic[13] 43.225 1.299 40.704 43.152 45.836
beta3_pelagic[14] 42.644 1.646 39.319 42.537 45.771
beta3_pelagic[15] 43.074 0.301 42.337 43.093 43.601
beta3_pelagic[16] 42.302 1.188 39.100 42.643 43.782
mu_beta0_pelagic[1] 0.874 0.939 -1.118 0.928 2.644
mu_beta0_pelagic[2] 1.776 0.364 1.007 1.783 2.493
mu_beta0_pelagic[3] 0.166 0.501 -0.881 0.186 1.094
tau_beta0_pelagic[1] 0.621 0.612 0.053 0.428 2.268
tau_beta0_pelagic[2] 2.940 3.257 0.258 2.076 10.590
tau_beta0_pelagic[3] 1.361 1.035 0.152 1.107 3.929
beta0_yellow[1] -0.555 0.205 -1.017 -0.535 -0.223
beta0_yellow[2] 0.416 0.282 -0.514 0.452 0.798
beta0_yellow[3] -0.342 0.220 -0.928 -0.323 0.011
beta0_yellow[4] 0.759 0.414 -0.532 0.866 1.221
beta0_yellow[5] -0.372 0.347 -1.049 -0.372 0.322
beta0_yellow[6] 1.107 0.166 0.791 1.102 1.438
beta0_yellow[7] 1.018 0.160 0.705 1.016 1.328
beta0_yellow[8] 0.987 0.157 0.678 0.990 1.287
beta0_yellow[9] 0.657 0.158 0.347 0.658 0.959
beta0_yellow[10] 0.584 0.144 0.304 0.585 0.862
beta0_yellow[11] -1.660 0.729 -2.956 -1.683 -0.344
beta0_yellow[12] -3.731 0.532 -4.910 -3.715 -2.735
beta0_yellow[13] -3.663 0.430 -4.773 -3.616 -2.993
beta0_yellow[14] -1.524 0.929 -2.877 -1.827 -0.060
beta0_yellow[15] -2.663 0.469 -3.465 -2.706 -1.598
beta0_yellow[16] -2.054 0.737 -3.270 -2.224 -0.392
beta1_yellow[1] 0.642 0.506 0.007 0.558 1.874
beta1_yellow[2] 1.143 0.532 0.557 1.024 2.930
beta1_yellow[3] 0.755 0.331 0.213 0.712 1.663
beta1_yellow[4] 1.464 0.791 0.624 1.205 3.839
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 1.870 0.773 0.398 2.005 3.149
beta1_yellow[12] 2.568 0.566 1.490 2.552 3.857
beta1_yellow[13] 2.818 0.441 2.174 2.762 3.923
beta1_yellow[14] 1.675 0.844 0.330 1.910 2.996
beta1_yellow[15] 1.955 0.458 0.913 2.018 2.736
beta1_yellow[16] 1.820 0.740 0.175 2.027 2.991
beta2_yellow[1] -3.480 2.719 -8.467 -3.167 -0.051
beta2_yellow[2] -2.491 2.182 -6.937 -1.728 -0.055
beta2_yellow[3] -1.781 2.126 -7.737 -1.129 -0.088
beta2_yellow[4] -2.345 2.766 -9.819 -1.238 -0.086
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.639 2.822 -11.631 -3.994 -1.000
beta2_yellow[12] -4.928 2.699 -11.412 -4.332 -1.240
beta2_yellow[13] -4.779 2.595 -11.293 -4.213 -1.571
beta2_yellow[14] -4.756 2.755 -11.384 -4.285 -0.704
beta2_yellow[15] -4.523 2.741 -11.471 -3.873 -1.148
beta2_yellow[16] -4.942 2.714 -11.451 -4.393 -1.115
beta3_yellow[1] 27.415 7.682 18.340 24.461 44.483
beta3_yellow[2] 29.499 2.494 25.280 29.036 35.331
beta3_yellow[3] 32.676 3.657 23.556 32.602 41.177
beta3_yellow[4] 29.525 3.934 23.063 28.240 39.899
beta3_yellow[5] 30.210 7.986 18.420 29.374 44.937
beta3_yellow[6] 29.856 7.958 18.492 28.656 44.862
beta3_yellow[7] 30.082 7.834 18.534 29.268 44.736
beta3_yellow[8] 30.200 7.994 18.468 29.276 45.001
beta3_yellow[9] 30.149 8.010 18.457 29.307 45.067
beta3_yellow[10] 30.339 8.034 18.417 29.521 44.897
beta3_yellow[11] 44.960 1.316 42.266 45.238 45.961
beta3_yellow[12] 43.292 0.381 42.528 43.270 44.016
beta3_yellow[13] 44.862 0.402 44.013 44.935 45.577
beta3_yellow[14] 41.686 4.259 33.404 43.874 45.773
beta3_yellow[15] 45.032 0.538 43.998 45.015 45.939
beta3_yellow[16] 44.273 1.544 39.894 44.474 45.847
mu_beta0_yellow[1] 0.066 0.549 -0.991 0.070 1.219
mu_beta0_yellow[2] 0.637 0.344 -0.092 0.652 1.282
mu_beta0_yellow[3] -2.154 0.792 -3.352 -2.284 -0.304
tau_beta0_yellow[1] 3.039 7.721 0.093 1.272 18.483
tau_beta0_yellow[2] 3.145 3.752 0.295 2.132 11.426
tau_beta0_yellow[3] 1.076 1.355 0.075 0.582 4.660
beta0_black[1] -0.080 0.158 -0.395 -0.081 0.235
beta0_black[2] 1.917 0.129 1.665 1.914 2.173
beta0_black[3] 1.315 0.135 1.050 1.316 1.579
beta0_black[4] 2.427 0.134 2.163 2.428 2.674
beta0_black[5] 4.557 2.019 1.834 4.141 9.618
beta0_black[6] 4.605 1.913 2.223 4.159 9.541
beta0_black[7] 3.754 1.851 1.528 3.297 8.546
beta0_black[8] 0.979 0.212 0.563 0.979 1.388
beta0_black[9] 2.607 0.235 2.144 2.609 3.058
beta0_black[10] 1.462 0.133 1.207 1.463 1.717
beta0_black[11] 3.490 0.161 3.170 3.490 3.808
beta0_black[12] 4.867 0.179 4.499 4.868 5.212
beta0_black[13] -0.121 0.240 -0.619 -0.113 0.321
beta0_black[14] 2.860 0.162 2.543 2.866 3.175
beta0_black[15] 1.291 0.150 1.000 1.292 1.585
beta0_black[16] 4.278 0.163 3.956 4.277 4.607
beta2_black[1] 7.589 9.687 0.569 3.498 37.517
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.894 1.526 -6.157 -1.412 -0.410
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.789 1.060 39.939 41.951 43.210
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.230 0.771 37.456 39.294 40.541
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.256 0.194 -0.645 -0.256 0.124
beta4_black[2] 0.240 0.187 -0.142 0.238 0.603
beta4_black[3] -0.929 0.194 -1.292 -0.930 -0.534
beta4_black[4] 0.426 0.219 -0.002 0.416 0.851
beta4_black[5] 0.555 1.381 -1.331 0.355 3.548
beta4_black[6] 0.565 1.328 -1.295 0.346 3.773
beta4_black[7] 0.462 1.242 -1.464 0.294 3.528
beta4_black[8] -0.268 0.321 -0.896 -0.267 0.341
beta4_black[9] 0.838 0.784 -0.258 0.683 2.778
beta4_black[10] 0.045 0.188 -0.317 0.044 0.418
beta4_black[11] -0.694 0.221 -1.131 -0.694 -0.259
beta4_black[12] 0.173 0.327 -0.460 0.167 0.833
beta4_black[13] -1.185 0.227 -1.623 -1.182 -0.746
beta4_black[14] -0.181 0.235 -0.624 -0.183 0.298
beta4_black[15] -0.886 0.208 -1.298 -0.889 -0.490
beta4_black[16] -0.600 0.232 -1.054 -0.600 -0.143
mu_beta0_black[1] 1.294 0.906 -0.573 1.331 3.006
mu_beta0_black[2] 2.703 1.086 0.744 2.605 5.156
mu_beta0_black[3] 2.550 0.999 0.423 2.594 4.422
tau_beta0_black[1] 0.618 0.578 0.056 0.443 2.134
tau_beta0_black[2] 0.469 0.679 0.046 0.256 2.087
tau_beta0_black[3] 0.236 0.155 0.051 0.197 0.620
beta0_dsr[11] -2.886 0.307 -3.474 -2.899 -2.248
beta0_dsr[12] 4.532 0.423 3.966 4.552 5.121
beta0_dsr[13] -1.372 0.503 -2.964 -1.288 -0.742
beta0_dsr[14] -3.858 0.519 -4.858 -3.879 -2.871
beta0_dsr[15] -1.948 0.429 -3.287 -1.876 -1.345
beta0_dsr[16] -3.023 0.384 -3.759 -3.014 -2.293
beta1_dsr[11] 4.863 0.325 4.224 4.879 5.495
beta1_dsr[12] 6.561 6.393 2.247 5.166 18.847
beta1_dsr[13] 2.941 0.626 2.296 2.824 4.935
beta1_dsr[14] 6.526 0.553 5.448 6.549 7.601
beta1_dsr[15] 3.462 0.723 2.745 3.321 6.009
beta1_dsr[16] 5.846 0.403 5.070 5.841 6.632
beta2_dsr[11] -8.030 2.297 -13.416 -7.694 -4.437
beta2_dsr[12] -6.688 2.593 -12.119 -6.526 -1.942
beta2_dsr[13] -5.917 2.853 -11.932 -5.912 -0.283
beta2_dsr[14] -5.730 2.579 -11.289 -5.574 -1.503
beta2_dsr[15] -6.933 2.746 -12.603 -6.867 -0.169
beta2_dsr[16] -7.415 2.237 -12.830 -7.012 -4.118
beta3_dsr[11] 43.481 0.147 43.208 43.476 43.765
beta3_dsr[12] 33.965 0.902 32.114 34.107 34.815
beta3_dsr[13] 43.251 0.381 42.721 43.169 44.172
beta3_dsr[14] 43.366 0.232 43.085 43.306 43.947
beta3_dsr[15] 43.396 0.893 42.949 43.493 43.931
beta3_dsr[16] 43.439 0.154 43.173 43.431 43.748
beta4_dsr[11] 0.549 0.217 0.137 0.545 0.978
beta4_dsr[12] 0.246 0.441 -0.655 0.238 1.111
beta4_dsr[13] -0.179 0.224 -0.611 -0.180 0.257
beta4_dsr[14] 0.153 0.250 -0.340 0.156 0.633
beta4_dsr[15] 0.676 0.219 0.270 0.674 1.120
beta4_dsr[16] 0.154 0.232 -0.290 0.156 0.596
beta0_slope[11] -1.824 0.144 -2.100 -1.826 -1.535
beta0_slope[12] -4.476 0.260 -4.998 -4.471 -3.983
beta0_slope[13] -1.294 0.155 -1.615 -1.294 -0.997
beta0_slope[14] -2.672 0.166 -2.998 -2.675 -2.350
beta0_slope[15] -1.332 0.150 -1.628 -1.333 -1.040
beta0_slope[16] -2.734 0.158 -3.048 -2.732 -2.418
beta1_slope[11] 4.472 0.220 4.041 4.473 4.912
beta1_slope[12] 3.969 0.459 3.087 3.967 4.888
beta1_slope[13] 2.639 0.241 2.187 2.631 3.129
beta1_slope[14] 6.327 0.413 5.511 6.317 7.143
beta1_slope[15] 3.006 0.214 2.600 3.006 3.436
beta1_slope[16] 5.289 0.291 4.729 5.284 5.872
beta2_slope[11] 8.674 2.328 5.044 8.326 14.134
beta2_slope[12] 6.850 2.914 1.212 6.900 12.919
beta2_slope[13] 5.861 2.864 1.260 5.794 11.862
beta2_slope[14] 6.620 2.600 2.367 6.526 12.225
beta2_slope[15] 8.133 2.234 4.432 7.825 13.106
beta2_slope[16] 7.860 2.263 4.333 7.553 13.250
beta3_slope[11] 43.459 0.133 43.217 43.456 43.720
beta3_slope[12] 43.354 0.284 42.896 43.310 43.930
beta3_slope[13] 43.458 0.312 42.990 43.423 43.989
beta3_slope[14] 43.262 0.143 43.089 43.224 43.629
beta3_slope[15] 43.490 0.162 43.192 43.485 43.801
beta3_slope[16] 43.372 0.146 43.149 43.349 43.702
beta4_slope[11] -0.745 0.166 -1.068 -0.744 -0.429
beta4_slope[12] -1.140 0.473 -2.181 -1.096 -0.318
beta4_slope[13] 0.071 0.159 -0.238 0.068 0.382
beta4_slope[14] -0.092 0.195 -0.478 -0.091 0.293
beta4_slope[15] -0.764 0.154 -1.062 -0.766 -0.467
beta4_slope[16] -0.163 0.177 -0.502 -0.163 0.186
sigma_H[1] 0.196 0.056 0.086 0.194 0.304
sigma_H[2] 0.175 0.030 0.120 0.173 0.238
sigma_H[3] 0.201 0.043 0.124 0.198 0.296
sigma_H[4] 0.386 0.073 0.263 0.378 0.552
sigma_H[5] 0.989 0.234 0.559 0.973 1.470
sigma_H[6] 0.279 0.185 0.013 0.256 0.697
sigma_H[7] 0.286 0.055 0.201 0.278 0.419
sigma_H[8] 0.447 0.121 0.295 0.424 0.733
sigma_H[9] 0.419 0.090 0.285 0.407 0.633
sigma_H[10] 0.225 0.046 0.145 0.221 0.328
sigma_H[11] 0.280 0.047 0.202 0.276 0.381
sigma_H[12] 0.454 0.176 0.206 0.440 0.803
sigma_H[13] 0.204 0.037 0.139 0.202 0.284
sigma_H[14] 0.453 0.087 0.304 0.447 0.643
sigma_H[15] 0.248 0.041 0.181 0.244 0.339
sigma_H[16] 0.248 0.050 0.166 0.243 0.364
lambda_H[1] 2.870 3.776 0.145 1.568 12.759
lambda_H[2] 9.618 9.583 0.827 6.801 34.659
lambda_H[3] 7.158 12.948 0.308 3.536 35.810
lambda_H[4] 0.007 0.005 0.001 0.006 0.019
lambda_H[5] 2.335 6.274 0.013 0.327 20.950
lambda_H[6] 8.230 16.221 0.009 1.294 58.029
lambda_H[7] 0.015 0.010 0.003 0.012 0.040
lambda_H[8] 3.289 8.116 0.000 0.003 24.683
lambda_H[9] 0.019 0.013 0.003 0.016 0.053
lambda_H[10] 0.359 1.109 0.030 0.193 1.363
lambda_H[11] 0.366 0.508 0.014 0.203 1.576
lambda_H[12] 6.077 7.584 0.301 3.665 25.788
lambda_H[13] 4.303 4.112 0.327 3.098 14.615
lambda_H[14] 3.510 3.973 0.281 2.292 14.430
lambda_H[15] 0.032 0.065 0.004 0.019 0.144
lambda_H[16] 3.888 5.352 0.224 2.204 18.327
mu_lambda_H[1] 4.442 1.932 1.249 4.296 8.599
mu_lambda_H[2] 3.370 1.955 0.226 3.238 7.450
mu_lambda_H[3] 3.891 1.855 1.054 3.626 8.012
sigma_lambda_H[1] 8.851 4.302 2.134 8.283 18.287
sigma_lambda_H[2] 7.873 4.909 0.353 7.223 18.092
sigma_lambda_H[3] 6.661 3.888 1.300 5.820 16.243
beta_H[1,1] 6.829 1.097 4.294 7.010 8.453
beta_H[2,1] 9.868 0.474 8.811 9.891 10.768
beta_H[3,1] 8.022 0.728 6.303 8.112 9.214
beta_H[4,1] 11.059 7.589 -3.935 11.093 26.061
beta_H[5,1] -0.059 3.166 -6.499 0.086 6.240
beta_H[6,1] 3.265 3.901 -6.648 4.561 7.600
beta_H[7,1] 1.538 5.458 -10.448 1.944 11.452
beta_H[8,1] 25.684 24.567 -2.597 27.788 66.542
beta_H[9,1] 13.699 5.453 3.379 13.328 24.941
beta_H[10,1] 7.223 1.678 3.790 7.245 10.792
beta_H[11,1] 6.044 3.127 -1.558 6.914 10.096
beta_H[12,1] 2.570 0.909 0.897 2.525 4.604
beta_H[13,1] 9.049 0.830 7.307 9.115 10.415
beta_H[14,1] 2.173 0.986 0.140 2.180 4.140
beta_H[15,1] -5.302 4.003 -12.346 -5.650 3.553
beta_H[16,1] 3.582 1.655 0.025 3.660 6.375
beta_H[1,2] 7.913 0.247 7.408 7.926 8.367
beta_H[2,2] 10.045 0.135 9.769 10.046 10.303
beta_H[3,2] 8.968 0.191 8.577 8.968 9.354
beta_H[4,2] 3.048 1.442 0.208 3.066 5.933
beta_H[5,2] 1.899 1.080 -0.209 1.907 3.958
beta_H[6,2] 5.821 1.061 3.338 5.994 7.437
beta_H[7,2] 2.344 1.058 0.419 2.273 4.655
beta_H[8,2] -2.740 5.573 -11.192 -4.205 4.182
beta_H[9,2] 2.968 1.004 1.043 2.961 4.966
beta_H[10,2] 8.122 0.360 7.339 8.139 8.756
beta_H[11,2] 9.597 0.576 8.788 9.463 11.003
beta_H[12,2] 3.956 0.345 3.292 3.956 4.652
beta_H[13,2] 9.191 0.225 8.774 9.191 9.625
beta_H[14,2] 4.067 0.356 3.362 4.069 4.751
beta_H[15,2] 11.239 0.710 9.795 11.271 12.555
beta_H[16,2] 5.454 0.844 3.728 5.479 6.995
beta_H[1,3] 8.555 0.248 8.119 8.545 9.072
beta_H[2,3] 10.130 0.111 9.918 10.125 10.365
beta_H[3,3] 9.652 0.163 9.336 9.649 9.990
beta_H[4,3] -1.735 0.952 -3.610 -1.717 0.181
beta_H[5,3] 4.147 0.727 2.660 4.167 5.529
beta_H[6,3] 8.048 1.155 6.507 7.682 10.689
beta_H[7,3] -2.395 0.665 -3.724 -2.381 -1.147
beta_H[8,3] 8.061 2.518 4.836 8.869 11.906
beta_H[9,3] -1.931 0.691 -3.314 -1.930 -0.608
beta_H[10,3] 8.867 0.285 8.299 8.861 9.432
beta_H[11,3] 8.674 0.271 8.064 8.697 9.146
beta_H[12,3] 5.373 0.294 4.725 5.397 5.857
beta_H[13,3] 9.067 0.172 8.744 9.063 9.407
beta_H[14,3] 5.875 0.267 5.298 5.892 6.359
beta_H[15,3] 10.479 0.328 9.858 10.482 11.130
beta_H[16,3] 7.427 0.416 6.522 7.460 8.140
beta_H[1,4] 8.308 0.177 7.936 8.321 8.617
beta_H[2,4] 10.200 0.109 9.961 10.209 10.394
beta_H[3,4] 10.162 0.154 9.830 10.175 10.434
beta_H[4,4] 11.701 0.420 10.844 11.700 12.532
beta_H[5,4] 6.087 0.983 4.493 5.981 8.269
beta_H[6,4] 7.307 0.812 5.246 7.541 8.336
beta_H[7,4] 8.196 0.341 7.495 8.207 8.843
beta_H[8,4] 5.800 0.949 4.176 5.687 7.120
beta_H[9,4] 7.004 0.400 6.235 7.002 7.823
beta_H[10,4] 7.799 0.259 7.316 7.791 8.370
beta_H[11,4] 9.428 0.197 9.045 9.425 9.810
beta_H[12,4] 7.144 0.208 6.740 7.145 7.581
beta_H[13,4] 9.191 0.159 8.889 9.188 9.525
beta_H[14,4] 7.840 0.205 7.439 7.841 8.259
beta_H[15,4] 9.515 0.239 9.045 9.517 9.989
beta_H[16,4] 9.196 0.176 8.873 9.184 9.583
beta_H[1,5] 8.988 0.143 8.705 8.991 9.266
beta_H[2,5] 10.793 0.091 10.617 10.792 10.977
beta_H[3,5] 10.909 0.168 10.608 10.896 11.263
beta_H[4,5] 8.428 0.428 7.558 8.424 9.296
beta_H[5,5] 5.011 0.846 3.072 5.153 6.304
beta_H[6,5] 8.709 0.578 7.872 8.573 10.197
beta_H[7,5] 6.836 0.320 6.222 6.836 7.495
beta_H[8,5] 8.893 0.733 7.877 8.847 10.288
beta_H[9,5] 8.303 0.400 7.518 8.303 9.071
beta_H[10,5] 10.065 0.242 9.572 10.067 10.537
beta_H[11,5] 11.480 0.230 11.023 11.483 11.925
beta_H[12,5] 8.456 0.187 8.089 8.457 8.829
beta_H[13,5] 10.053 0.127 9.799 10.051 10.308
beta_H[14,5] 9.209 0.208 8.820 9.206 9.635
beta_H[15,5] 11.170 0.253 10.666 11.171 11.658
beta_H[16,5] 9.957 0.145 9.671 9.957 10.243
beta_H[1,6] 10.186 0.189 9.850 10.178 10.614
beta_H[2,6] 11.503 0.105 11.306 11.499 11.718
beta_H[3,6] 10.822 0.158 10.473 10.830 11.104
beta_H[4,6] 12.870 0.753 11.281 12.879 14.325
beta_H[5,6] 6.056 0.761 4.741 5.980 7.754
beta_H[6,6] 8.702 0.612 6.949 8.808 9.557
beta_H[7,6] 9.834 0.523 8.793 9.854 10.840
beta_H[8,6] 8.584 1.061 6.402 8.855 9.905
beta_H[9,6] 8.406 0.665 7.088 8.386 9.735
beta_H[10,6] 9.534 0.324 8.851 9.559 10.094
beta_H[11,6] 10.884 0.333 10.182 10.908 11.479
beta_H[12,6] 9.377 0.245 8.908 9.372 9.874
beta_H[13,6] 11.078 0.151 10.810 11.072 11.389
beta_H[14,6] 9.808 0.258 9.289 9.806 10.314
beta_H[15,6] 10.871 0.423 10.037 10.884 11.700
beta_H[16,6] 10.633 0.178 10.267 10.639 10.974
beta_H[1,7] 10.853 0.879 8.803 10.961 12.315
beta_H[2,7] 12.192 0.424 11.302 12.196 13.021
beta_H[3,7] 10.591 0.651 9.135 10.658 11.698
beta_H[4,7] 2.524 3.882 -4.827 2.445 10.532
beta_H[5,7] 7.054 2.706 2.157 6.724 13.145
beta_H[6,7] 9.376 2.356 4.985 9.261 15.595
beta_H[7,7] 10.740 2.605 5.674 10.712 15.839
beta_H[8,7] 14.637 4.726 8.923 12.648 25.101
beta_H[9,7] 4.574 3.418 -2.244 4.604 11.497
beta_H[10,7] 9.805 1.466 7.177 9.716 13.011
beta_H[11,7] 10.867 1.599 8.024 10.751 14.440
beta_H[12,7] 10.105 0.833 8.303 10.201 11.570
beta_H[13,7] 11.729 0.720 10.092 11.809 12.831
beta_H[14,7] 10.368 0.859 8.535 10.420 11.918
beta_H[15,7] 11.915 2.181 7.749 11.876 16.403
beta_H[16,7] 11.657 0.775 10.354 11.570 13.511
beta0_H[1] 8.590 14.040 -20.916 8.972 34.156
beta0_H[2] 10.824 6.257 -1.844 10.668 23.472
beta0_H[3] 10.074 9.079 -8.456 9.950 28.839
beta0_H[4] 12.683 175.633 -344.098 16.442 367.968
beta0_H[5] 4.549 40.077 -75.001 4.235 90.350
beta0_H[6] 9.228 47.823 -90.657 7.992 112.552
beta0_H[7] 9.732 126.235 -239.122 8.677 278.717
beta0_H[8] 6.973 289.953 -684.140 6.608 640.315
beta0_H[9] 5.801 109.532 -220.423 5.444 230.747
beta0_H[10] 9.474 33.172 -56.699 9.339 79.264
beta0_H[11] 10.134 42.274 -78.857 10.749 101.100
beta0_H[12] 6.969 9.554 -11.706 6.916 25.724
beta0_H[13] 10.046 9.821 -7.371 9.691 28.976
beta0_H[14] 6.951 11.087 -15.365 7.176 28.740
beta0_H[15] 7.396 104.611 -202.723 7.615 229.601
beta0_H[16] 8.349 11.295 -13.390 8.447 33.003